The width of a rectangle is 9 inches less than 4 times the length. If x represents the length, how do you write an algebraic expression in terms of x that represents the area of the rectangle?

1 Answer
Mar 20, 2016

Answer:

Area#=4x^2-9x#

Explanation:

We will convert the variable to include #x# afterwards

Breaking down the question into its component parts

Let width be #W#
Let length be #L#
Let area be #A#

The width of a rectangle #->W#
is #->W=?#
9 inches less than#->W=?-9#
4 times#->W=(4xx?)-9#
the length#->W=(4xxL)-9#

If x represents length#->W=(4xxx)-9#

Width#->color(green)(W=4x-9)#

Area is calculated by #color(green)("width")# times #color(magenta)("length")#.

In this case #A=color(green)(W)color(magenta)(x)#

Substituting for width gives

#A=color(green)((4x-9))color(magenta)(x)#

Multiplying out the bracket gives

#A=4x^2-9x#